The Worst Card-Sort Ever
Characteristics of Parent Functions SOLs AII.6 and AII.7
Teacher Notes – This assignment was originally conceived as a card-sort, but with 8 pages (originally), 18 cards per page,
it would be a nightmare for anyone to keep track of all of the cards. I used an earlier version this (7 stations, no scissors)
in one of my Algebra 2 classes for a review, and it took too long (>70 minutes). The class liked it and wanted to finish it
so we brainstormed how to make it better, and this is what we came up with. (Some suggestions have been
incorporated in the assignment and are not described.)
1. Give each student a “Graphs” page. Students found it helpful to write the functions and numbers on the graphs
and have their own copy.
2. Point out to students that cards with the same number or letter contain different ways to say the same thing.
3. Give each group a copy of the answer sheet and have them complete the “Graphs” column of the table first.
(Students agreed the rest was easier once they had the graphs sorted.)
4. The rest of the assignment could then be done using 6 stations, but a block may not be enough time.
5. The tables are particularly challenging (because of the logs and non-functions.)
6 Stations – Place a couple of copies of each of the sheets 4, 5, 6, 8, 9, 10 in sheet protectors and place the (identical)
sheets in a colored folder. (I used two or three copies so each student can have a sheet while working. I also made 2 of
each station and placed the sheets in the same color folders. Students knew they had to do every color station.)
Students liked using dry erase markers to mark on sheet protectors and erase when done.
The assignment can be simplified or shortened by eliminating some functions or topics. On the key, find the numbers for
the cards you wish to delete and delete the contents of those cells or entire pages. (For example, if you haven’t gotten
to inverses yet, delete that page.) The exponential and logarithm cards could be eliminated. (Empty the contents of
those cells before printing – use the KEY, rows 15-18, to see what to eliminate. Be careful not to change the numbering
or the key will be off.)
Table of Contents (page#)
2. Answer sheet (table)
3. Graphs of relations (Note that the graphs of inverses are one above the other.)
4. Domain & Range
5. End Behavior (uses x  0 notation, but explains notation)
6 and 7. Increasing, Decreasing and Constant Intervals (Algebra 2 and MAA versions)
8. Intercepts, Roots, Zeros, or Solutions, Asymptotes
9. Table
10. Inverse Relation
11. Key
12-17 Fill-in-the-blank pages if you want students to complete, so they have info in notebook. This would be a long
assignment to do all at once. We did not use these.
The Worst Card Sort Assignment Ever
Name ________________________________________________
SOL AII.6 and AII.7 (Function Properties)
Date __________________________
Period _____________
Directions: Complete the table as you match functions with their graphs, domains, ranges, end behaviors, increasing,
decreasing and constant intervals, intercepts, roots, zeros or solutions, and asymptotes, tables and inverses.
Function or
Relation
1.
f ( x)  x
2.
x0
3.
x y
4.
f ( x)  x 2 ,
x0
5.
f ( x)  0
6.
f ( x)  3 x
7.
f ( x)   x
8.
f ( x)  x
9.
f ( x)  x 2
10. f ( y )  y
11. f ( x)  x3
12. f ( x)  a
13. f ( x) 
x
14. x  a
15.
f ( x)  logb x,
b 1
f ( x)  b x ,
16.
b 1
f ( x)  b x ,
17.
0  b 1
f ( x)  logb x,
18.
0  b 1
Graph
Domain &
Range
End
Behavior
Increasing, Intercepts,
Decreasing,
Roots,
Constant
Zeros,
Intervals
Asymptotes
Table
Inverse
Relation
Graphs
A.
B.
C.
D.
E.
F.
G.
H.
I.
K.
This function is its own
inverse!
J.
L.
M.
N.
O.
P.
Q.
R.
Domain & Range - Note that there are four I’s, two II’s, two III’s, two IV’s, etc.
I.
I.
Domain:
Domain:
Range:
Range:
I.
II.
Domain: all real numbers
Domain:
Range: all real numbers
Range:
III.
Domain:
III.
x | 0  x  
Domain:
Range:
Range:
 y | 0  y  
IV.
Domain:
Range:
0,  
 ,  
VI.
V.
Domain:
Range:
 ,  
 ,  
 ,  
0,  
0,  
0,  
 0,  
 ,  
VI.
Domain:
Range:
 y : 0  y  
VIII.
a
Range:  ,  
Domain:
 ,  
Range:  0,  
Domain:
IX.
 ,  
Range: 0
Domain:
I.
Domain:
x |   x  
Range:
 y |   y  
II.
Domain:
Range:
 y | 0  y  
IV.
Domain:
x : 0  x  
Range:
V.
Domain:
x : 0  x  
Range:
VII.
Domain:
0
Range:
X.
Domain:
Range:
a
End Behavior - Note that there are fourAA’s, two BB’s, two HH’s, and two MM’s.
AA
AA
AA
As
x   , y   
As x gets more negative, y gets
more negative.
As x decreases without bound, y
decreases without bound.
x
As x gets larger, y gets larger.
As x increases without bound, y
increases without bound.
AA
BB
BB
This function goes up to the
right and down to the left.
As x decreases without bound, y
increases without bound.
As
As
, y  
As x increases without bound, y
increases without bound.
As
x   , y  
x  , y  
CC
DD
EE
As x decreases without bound, y
approaches 0.
As
As x decreases without bound, y
increases without bound.
As x increases without bound, y
approaches 0.
As
FF
GG
HH
As
As y decreases without bound, x
approaches a.
As x approaches 0 from the
right, y approaches 0.
As y increases without bound, x
approaches a.
As x increases without bound, y
increases without bound.
JJ
As x approaches 0 from the
right, y increases without bound.
KK
As x approaches 0 from the
positive direction, y decreases
without bound.
As x increases without bound, y
decreases without bound.
As x increases without bound, y
increases without bound.
LL
MM
MM
As
As
y   , x  
As y decreases without bound, x
increases without bound.
y  , x  
As y increases without bound, x
increases without bound.
As
y   , x  0
y
, x  0
HH
As

x 0 ,y 0
As
x  , y  
x   , y  0
x  , y  
As x increases without bound, y
approaches 0.
+ “from the right/positive direction”
As
x   , y  a
x  , y  a
As
Increasing , Decreasing, … Note that there are five R’s, two V’s, two W’s, four X’s, & two Y’s. (Alg. 2 version)
R. This function is
increasing for all real
numbers.
R. This function is
increasing for all real
numbers.
R. This function is
increasing for all real
numbers.
R. This function is
increasing for all real
numbers.
R. This function is
increasing for all real
numbers.
S. This function is
decreasing for all real
numbers.
T. This function is
decreasing for all
positive real numbers.
U. This function is
increasing for all x  0 .
V. This function is
increasing for all x  0 .
V. This function is
increasing for all nonnegative real numbers.
W. This function is constant
for all real numbers.
W. This function is neither
increasing nor
decreasing for all real
numbers.
X. This relation is not a
function.
X. There exists an x value
that has more than one
y value for this relation.
X. There exists a vertical
line that intersects the
graph of this relation at
more than one point.
X. This relation is not a
function.
Y. This function is
increasing on  0,  
and decreasing on
 ,0 .
Y. This function is
increasing for all positive
real numbers and
decreasing for all
negative real numbers.
(MAA Version) Increasing , Decreasing, … Note that there are five R’s, two V’s, two W’s, four X’s (one is a XX), & two Y’s.
R. For all real numbers a
and b, the slope of the
line through the points
 a, f (a)  and
R. This function is
increasing for all real
numbers.
(means f is increasing on
(a and b are real numbers.)
)
S. This function is
decreasing for all real
numbers.
f (a )  f (b)
0
a b
(means f is increasing on
)
)
R. For all real numbers a
and b,
a  b iff f (a )  f (b)
(means f is increasing on
(a and b are real numbers.)
b, f (b)  is greater
than 0.
(means f is increasing on
R.
R. a  b iff f (a)  f (b)
)
T. This function is
decreasing for all
positive real numbers.
U. This function is
increasing for all x  0 .
V. This function is
increasing for all x  0 .
V. This function is
increasing for all nonnegative real numbers.
W. This function is neither
increasing nor
decreasing for all real
numbers.
W. This function is constant
for all real numbers.
X. This relation is not a
function.
X. There exists an x value
that has more than one
y value for this relation.
X. There exists a vertical
line that intersects the
graph of this function at
more than one point.
X. The points (1,1) and
(1, 1) are both
members of this
relation, so this relation
is not a function.
Y. This function is
increasing on  0,  
and decreasing on
 ,0 .
Y. This function is
increasing for all positive
real numbers and
decreasing for all
negative numbers.
Intercepts, Roots or Zeros, Asymptotes - Note that there are eight1001’s and two 1002’s 1003’s and 1008’s.
1001.
This function has x- and
y-intercept (0, 0) .
The only zero of this
function is 0. It has no
asymptotes.
1001.
This function has x- and
y-intercept (0, 0) .
The only zero of this
function is 0. It has no
asymptotes.
1001.
This function has x- and
y-intercept (0, 0) .
The only zero of this
function is 0. It has no
asymptotes.
1001.
This function has x- and
y-intercept (0, 0) .
The only root of this
function is 0. It has no
asymptotes.
1001.
This function has x- and
y-intercept (0, 0) .
The only root of this
function is 0. It has no
asymptotes.
1001.
This function has x- and
y-intercept (0, 0) .
The only root of this
function is 0. It has no
asymptotes.
1001.
This function has x- and
y-intercept (0, 0) .
The only solution of this
function is 0. It has no
asymptotes.
1001.
This function has x- and
y-intercept (0, 0) .
The only solution of this
function is 0. It has no
asymptotes.
1002.
This function has yintercept (0,1) and
horizontal asymptote
y  0 . It has no zeros.
1002.
This function has yintercept (0,1) and
horizontal asymptote
y  0 . f ( x)  0 has no
solutions.
1003.
This function has xintercept (1, 0) and
vertical asymptote
x  0 . (1, 0) is also the
only root.
1003.
This function has xintercept (1, 0) and
vertical asymptote
x  0 . (1, 0) is also the
only solution.
1004.
This function has yintercept (0, a) . It has
no asymptotes, no roots,
and no x-intercepts.
1005.
This function has yintercept (0, 0) . Every
point is an x-intercept.
This function has no
asymptotes. Every xvalue is a zero.
1006.
This relation has xintercept (a, 0) . It has
no asymptotes and no yintercepts.
1007.
This relation has xintercept (0, 0) . Every
point is a y-intercept.
1008.
This relation is not a
function. It has exactly
one x- and y-intercept
(0, 0) .
1008.
This relation is not a
function. It’s only x- and
y-intercept is at the
origin.
This relation has no
asymptotes.
It does not have any
asymptotes.
It does not have any
asymptotes.
Tables
T1.
T2.
x
-2
-1
0
1
2
f(x)
a
a
a
a
a
T4.
T3.
x
-8
-1
0
1
8
f(x)
-2
-1
0
1
2
T5.
x
0
1
x
-2
-1
0
1
2
f(x)
2
1
0
1
2
x
a
a
a
a
a
y
-2
-1
0
1
2
T6.
2
f(x)
-2
-1
0
1
2
x
-2
-1
0
1
2
f(x)
0
0
0
0
0
x
-2
-1
0
1
2
f(x)
-2
-1
0
1
2
x
-8
-1
0
1
8
f(x)
-8
-1
0
1
8
T10.
x
-2
-1
0
1
2
f(x)
-8
-1
0
1
8
T11.
x
2
1
0
1
2
y
-2
-1
0
1
2
T12.
x
-2
-1
0
1
2
f(x)
4
1
0
1
4
T13.
x
0
0
0
0
0
y
-2
-1
0
1
2
T14.
x
-2
-1
0
1
2
Note b = 2
f(x)
0.25
0.5
1
2
4
T15.
x
0.25
0.5
1
2
4
Note b = 2
f(x)
-2
-1
0
1
2
T17.
x
-2
-1
0
1
2
Note b  1/ 2
f(x)
4
2
1
0.5
0.25
T18.
x
4
2
1
0.5
0.25
Note b  1/ 2
y
-2
-1
0
1
2
T7.
x
4
1
0
1
4
y
-2
-1
0
1
2
T8.
T16.
x
-2
-1
0
1
2
f(x)
0
1
2
T8.
Inverse Relation
82.
81.
83.
This function is the
inverse of the function
This function is the
inverse of the function
f ( x)  x 2 , x  0
86.
This relation is the
inverse of the
This function is the
inverse of the function
88.
f ( x)  a
This function is the
inverse of the function
89.
f ( x)  0
95.
This function is the
inverse of the function
x y
This function is the
inverse of the function
f ( x)  logb x, b  1
f ( x)  x
97.
xa
This relation is the
inverse of the function
This function is the
inverse of itself.
94.
This function is the
inverse of the relation
f ( x)  x 2
92.
90.
This function is the
inverse of the relation
96.
This relation is the
inverse of the function
y x
f ( x)  x
93.
f ( x)  b x , b  1
This function is the
inverse of the relation
This relation is the
inverse of the function
90.
This function is the
inverse of the function
f ( x)  x
f ( x)  logb x, 0  b  1
87.
f ( x)  b x , 0  b  1
f ( x)  3 x
85.
84.
This function is the
inverse of the function
98.
This function is the
inverse of the function
f ( x)  x 3
This function is the
inverse of the relation
x0
KEY KEY KEY KEY KEY KEY KEY KEY KEY KEY KEY KEY KEY KEY KEY KEY KEY KEY KEY KEY KEY KEY KEY KEY KEY KEY KEY KEY
Increasing, Intercepts,
Decreasing,
Roots,
Constant
Zeros,
Intervals
Asymptotes
Function or
Relation
Graph
Domain &
Range
End
Behavior
1.
f ( x)  x
H or K
I
AA
R
2.
x0
D
VII
FF
3.
x y
P
IV
L
4.
f ( x)  x 2 ,
x0
Table
Inverse
Relation
1001
T8
90
X
1007
T13
92
MM
X
1008
T11
85
III
HH
V
1001
T4
94
5.
f ( x)  0
A
IX
CC
W
1005
T7
98
6.
f ( x)  3 x
J
I
AA
R
1001
T2
97
7.
f ( x)   x
F
IV
MM
X
1008
T5
89
8.
f ( x)  x
M
II
BB
Y
1001
T3
93
9.
f ( x)  x 2
C
II
BB
Y
1001
T12
88
10. f ( y )  y
H or K
I
AA
R
1001
T8
90
11. f ( x)  x3
G
I
AA
R
1001
T10
82
12. f ( x)  a
B
X
LL
W
1004
T1
96
I
III
HH
V
1001
T16
81
E
VIII
GG
X
1006
T6
87
Q
V
KK
U
1003
T15
86
N
VI
DD
R
1002
T14
95
O
VI
EE
S
1002
T17
84
R
V
JJ
T
1003
T18
83
13. f ( x) 
x
14. x  a
15.
f ( x)  logb x,
b 1
f ( x)  b x ,
16.
b 1
f ( x)  b x ,
17.
0  b 1
f ( x)  logb x,
18.
0  b 1
The Worst Card Sort Assignment Ever
SOL AII.6 & 7 (Parent Function Properties)
Notebook Version
Name ________________________________________
Date ________________________
Period_________
Directions: Complete the tables.
1.
Domain and Range
2.
Domain and Range
3.
Domain and Range
End Behavior
End Behavior
End Behavior
Increasing, Decreasing and
Constant Intervals
Increasing, Decreasing and
Constant Intervals
Increasing, Decreasing and
Constant Intervals
Inverse relation
Inverse relation
Inverse relation
Sketch the graph of the inverse
relation on the graph above.
Sketch the graph of the inverse
relation on the graph above.
Sketch the graph of the inverse
relation on the graph above.
Intercepts, Asymptotes
Intercepts, Asymptotes
Intercepts, Asymptotes
Table
Table
Table
The Worst Card Sort Assignment Ever
(page 2)
Directions: Complete the table.
6.
4.
Domain and Range
5.
Domain and Range
Domain and Range
End Behavior
End Behavior
End Behavior
Increasing, Decreasing and
Constant Intervals
Increasing, Decreasing and
Constant Intervals
Increasing, Decreasing and
Constant Intervals
Inverse relation
Inverse relation
Inverse relation
Sketch the graph of the inverse
relation on the graph above.
Sketch the graph of the inverse
relation on the graph above.
Sketch the graph of the inverse
relation on the graph above.
Intercepts, Asymptotes
Intercepts, Asymptotes
Intercepts, Asymptotes
Table
Table
Table
The Worst Card Sort Assignment Ever
(page 3)
Directions: Complete the table.
9.
7.
Domain and Range
8.
Domain and Range
Domain and Range
End Behavior
End Behavior
End Behavior
Increasing, Decreasing and
Constant Intervals
Increasing, Decreasing and
Constant Intervals
Increasing, Decreasing and
Constant Intervals
Inverse relation
Inverse relation
Inverse relation
Sketch the graph of the inverse
relation on the graph above.
Sketch the graph of the inverse
relation on the graph above.
Sketch the graph of the inverse
relation on the graph above.
Intercepts, Asymptotes
Intercepts, Asymptotes
Intercepts, Asymptotes
Table
Table
Table
The Worst Card Sort Assignment Ever
(page 4)
Directions: Complete the table.
11.
This function is its own
inverse!
10.
12.
Domain and Range
Domain and Range
Domain and Range
End Behavior
End Behavior
End Behavior
Increasing, Decreasing and
Constant Intervals
Increasing, Decreasing and
Constant Intervals
Increasing, Decreasing and
Constant Intervals
Inverse relation
Inverse relation
Inverse relation
Sketch the graph of the inverse
relation on the graph above.
Sketch the graph of the inverse
relation on the graph above.
Sketch the graph of the inverse
relation on the graph above.
Intercepts, Asymptotes
Intercepts, Asymptotes
Intercepts, Asymptotes
Table
Table
Table
The Worst Card Sort Assignment Ever
(page 5)
Directions: Complete the table.
15.
13.
Domain and Range
14.
Domain and Range
Domain and Range
End Behavior
End Behavior
End Behavior
Increasing, Decreasing and
Constant Intervals
Increasing, Decreasing and
Constant Intervals
Increasing, Decreasing and
Constant Intervals
Inverse relation
Inverse relation
Inverse relation
Sketch the graph of the inverse
relation on the graph above.
Sketch the graph of the inverse
relation on the graph above.
Sketch the graph of the inverse
relation on the graph above.
Intercepts, Asymptotes
Intercepts, Asymptotes
Intercepts, Asymptotes
Table
Table
Table
The Worst Card Sort Assignment Ever
(page 6)
Directions: Complete the table.
17.
18.
16.
Domain and Range
Domain and Range
Domain and Range
End Behavior
End Behavior
End Behavior
Increasing, Decreasing and
Constant Intervals
Increasing, Decreasing and
Constant Intervals
Increasing, Decreasing and
Constant Intervals
Inverse relation
Inverse relation
Inverse relation
Sketch the graph of the inverse
relation on the graph above.
Sketch the graph of the inverse
relation on the graph above.
Sketch the graph of the inverse
relation on the graph above.
Intercepts, Asymptotes
Intercepts, Asymptotes
Intercepts, Asymptotes
Table
Table
Table